The fundamental idea behind developing a maximally expressive AgentNet implementation is to ensure that the functions learnt by the agent are injective. A similar proof technique for developing injective GNN implementations has already been applied to analyze the expressive power of standard GNNs [1]} and also some GNN extensions [2]}; we refer the reader to these papers for more technical details on this proof approach. As in the rest of these proofs, we assume that the range of the node features is a finite set, and we also have a finite upper bound on the maximal degree \(\Delta \)  of the graph. With an induction, this already shows that after any finite number of time steps \(t\) , the range of possible embeddings (of agents or nodes) is still finite.
